Comparison of the Reference Unit Method and Dimensional Analysis Methods for Two Large Shrubby Species in the Caatinga Woodlands
ROBERT D. KIRMSE AND BRIEN E. NORTON
Abstract
The reference unit technique was compared with the dimensional analysis approach for estimating large shrub foliige biomass
in Northeast Brazil. The techniques were tested on coppicing
jurema (Mhosa acutistipula Benth.) and pau branco (Auxemma
oncocalyx [Fr. Alem.] Taub.). Both methods provided good estimates of foliage weight. The coeffkients of determination for the
reference unit approach ranged from .890 to .985. The P values
obtained in applying the dimensional analysis method were .937
and .948. Improvements
in estimates with the reference unit
method were obtained when (1) a branch unit of 19% of total plant
foliage was used versus a unit of only 7%, (2) the branch unit
resembled the appearance of the branching of the plant being
estimated, and (3) estimations of 3 judges were averaged.
Total foliage production on shrubs and trees is one of the most
difficult parameters to measure or estimate on native rangelands.
The woody material and variable growth form renders most traditional sampling methods, largely derived for agronomic conditions, impractical for shrubs. As a consequence, vegetation sampling technique manuals ha,ve made only passing reference to or
given insignificant information on biomass estimation of shrub
foliage or current growth (Brown 1954, NAS 1962, Newbold 1967,
Pieper 1973, t’Mannetje 1978). Efficient estimations of browse
availability are required for research on brush control and grazing
animal diet studies.
Shrub measurement techniques used in other semiarid areas of
the world were examined with the prospect of adapting a suitable
method for the caatinga species. The criteria for selection were that
the method be nondestructive, time efficient, and relatively precise.
Traditional ‘clip-and-weigh’ methods (e.g., Whittaker 1961) were
eliminated from consideration
because of the labor and cost
required (Gimingham and Miller 1968, Rutherford 1979), and
because the associated research design did not permit destructive
sampling. The twig count method of Shafer (1963) and methods
relating foliage weight to the dimensions of individual branches
(Whittaker 1962, Ovington et al. 1963, Provenza and Urness 1981)
were considered inappropriate because of the high density of coppicing branches sprouting from the stumps of the test species.
Two sampling techniques were selected for testing on large
shrubs of Northeast Brazil. The first of these employs the principle
of matching standards against samples (Hutchinson et al. 1972,
Andrew et al. 1979), such as estimating the number of multiples of
the reference unit (e.g., leafy branch) present in the entire plant.
This technique was tested by Andrew et al. (1981) on 2 small
Australian shrubs (Atriplex vesicaria Heward ex Benth. and Maireana sedifolia F. Muell.) and compared favorably with other
techniques for estimating shrub biomass. The second technique,
dimensional analysis, requires establishing a relationship between
Authors
are research assistant and associate professor.
Department
of Range
Science, Utah State Universitv.
Logan 84322.
This research was carried oiti as iart of the United States Agency for International
Development
Title X11 Small Ruminants
Collaborative
Research Support Program
under Grant No. AID/
DSAN/
XWGaO49,
in collaboration
with the Empress Brasileira de Pesquisa Agropecuaria
(EMBRAPA),
Brazil. The support of the EMBAPA
staff is gratefully
acknowledged.
The authors would also like to thank Joao Queiroz
and Mireille
Kirmse for help with data collection,
Keith Owens and Alan Carpenter
for manuscript
review, and Drs. David Turner
and Fred Provenza
for advice on
statistical analysis.
Manuscript
accepted January
IO, 1985.
JOURNAL
OF RANGE
MANAGEMENT
38(5), September
1985
easily obtained plant dimensions and foliage weight. A number of
studies have shown that canopy volume is highly correlated with
foliage weight (Cook 1960, Ludwig et al. 1975, Uresk et al. 1977,
Lyon 1968, Kelley and Walker 1976, Bryant and Kothmann 1979,
Guy 1981).
Study
Area and Methods
The study area was located in Ceara State of Northeast Brazil
(3.Y south latitude, 41° west longitude), much of which is dominated by semiarid tropical woodland, called the caatinga (Pfister et
al. 1983). The test plants werejurema (Mimosa acutistipula Benth.)
and pau branco (Auxemma oncocalyx [Fr. Alem.] Taub.), 2 common and widely distributed species. Morphological characteristics, habitat preferences and management values of these 2 species
are described by Kirmse et al. (1983). Jurema is a thorny, small
evergreen leguminous tree and pau branco is a deciduous tree; both
readily coppice after being cut near ground level and develop a
shrubby growth form. Fifteen coppicing jurema and pau branco
plants were selected over a range of sizes. They graded in height
from .45 to 2.00 m for jurema and .55 to 1.70m for pau branco and
represented the range of sizes available for goat browsing. The
jurema plants had been cut 2 years previously; the pau branco
plants were first year resprouts. The field data were collected in
May, 1980, during the latter part of the rainy season.
Reference Unit Technique
The technique was tested by 3 observers (judges), 1 of which had
2 years previous experience sampling sagebrush (Artemisia tridentata Nutt.) biomass with the reference unit method. Prior to the
beginning of the trial the experienced judge trained the inexperienced observers. This training involved estimating and verifying
foliage biomass of 3 jurema shrubs of different sizes and was
completed in 2 hours.
Jurema
The reference unit method was easily adapted to jurema because
the growth form of a resprouted plant provided clearly distinguishable branches (Fig. 1). The procedure involved 3 steps:
I) Representative branches, selected from plants not being
tested, provided the reference units. The leafy growth on the
branch comprised the reference unit per se. Andrew et al.
(1979) suggested that the preferred size of the reference unit be
IO-20% of the foliage weight of the average sample plant.
Three branches (units) were used for jurema in this study. The
smallest weighed 36 g (dry weight of foliage) and represented
7% of the average foliage weight of the 15 test plants. Two
larger branches, each representing about 19% of the average
plant, were also used for estimating jurema. Of these larger
units, one had compacted branching and dense foliage typical
of the test plants and the other had more dispersed foliage. For
convenience, these 3 reference units will be referred to as small,
large-compacted, and large-dispersed.
2) The number of times the foliage of the reference unit was
replicated in the test plant was counted. Only the leaves were
considered in the biomass estimations. The estimations were
conducted in early morning in order to avoid any bias associated with wilting and curling of the leaves on these reference
425
of the group of test plants. The 15test plants ranged from 4 to 19 m
distance from the reference plant, and all were within visible range.
Eachjudge independently
estimated the foliage of the I5 test plants
as a multiple or a fraction of the reference plant. Estimated weight
per pau branco plant was calculated by multiplying the dry weight
of leaves on the reference plant by the multiple or fraction estimated for the test plant.
The above procedures
provide biomass data on an individual
plant basis only. Standing crop per unit area can be determined by
estimating the multiples of the reference unit within a sample plot
or by calculations
that incorporate
estimates of plant density.
These reference unit estimates were compared
with the actual
weights in the analysis described below.
Dimensional Analysis
1
I
.I
I
1.0
I
2.0
I
1.6
I
2.5
2.2m
Fig. 1. The inverted conicalgrowth
habit of a coppicing jurema (Mimosa
acutistipula).
The branch to the right represents a rypical unit usedfor
rhe reference unir merhod.
units. Each judge independently
estimated the 15 jurema plants
with the 3 different units. The reference unit counts were not
shared among judges during the sampling period.
3. The leaves from the reference unit were stripped and dried at
105” C for 24 hours and weighed. The total dry leaf biomass of
each jurema plant was estimated by multiplying the number of
units counted for a plant by the weight of the dry foliage in the
reference unit. Actual foliage weight on each of the 15test plants
was obtained by stripping all the leaves and determining
dry
weight.
Pau branco
The reference unit approach described forjurema was not suitable for pau branco because of its compact, dense, and unsegmented
growth form (Fig. 2) and therefore an entire plant was used instead
-
The 3 judges worked together to obtain dimensional
measurements of the 30 test plants. Two diameters (the longest and that
perpendicular
to the longest) and the foliage height were measured
for each plant.
Canopy volume was calculated using these dimensional
measurements. Jurema plants that resprout after cutting develop an
inverted conical growth habit (Fig. 1) similar to Larrea tridentata
Vail. (Ludwig et al. 1975). The jurema canopy volume was calculated as:
canopy
volume = l/3 nr? h
where:
r = radius
as l/2
the average of the 2 diameters
h = height
The shape of the pau branco canopy is cylindrical (Fig. 2). so
volume was calculated using the formula:
canopy volume = nr* h
where:
r = radius as I/2 the average of the 2 diameters
h = height
Statistical Analysis
The relationship between theactual weight (dependent variable)
and the estimated weight (independent
variable) for the reference
unit estimation,
and the actual weight and the canopy volume
(independent
variable) for the dimensional
analysis were established using simple linear regressions. Differences in the intercepts
and slopes were tested on the regression equations for the 3 judges
and, for jurema, the 3 unit sizes, to determine if pooling of data
points were possible. Multiple regression techniques were used to
determine the effects ofjudges, unit size (forjurema),
and distance
from the unit (in the case of the reference plant method for pau
branco). The suitability of the regression models was inferred from
graphic display of the data. If curvilinearity
was apparent,
log
transformations
and polynomial models were used to obtain the
best fit. The preferred equations were selected on the basis of the
coefficient of determination
(r2) and a plot of the residuals was used
to examine the consistency of error terms (Neter and Wasserman
1974).
1.35m
-1.0
-.5
Results and Discussion
.i
Fig. 2. The cylindricalgrowth
habit of a coppicingpau
1.0
branco
’
1.2m
(Auxemma
oncocalyx).
of a branch. Otherwise the procedure for estimating pau branco
foliage biomass was similar to the procedures described forjurema.
The reference plant was 1m high and growing roughly in the center
426
The test of regression coefficients for the estimation of jurema
showed no significant difference in slopes or intercepts among the 3
judges Q00.05) but there was a significant difference in the estimation using the 3 different reference unit sizes (Table I). This indicated that it would be possible to combine regression equations
rather than to fit one for each judge. The equations presented,
therefore, are for combined individual estimations
for each unit
size (n = 45). Another component
of the analysis included an
averaging of the estimations of the 3 judges for each unit size (n = I5
for each unit size). Averaging estimations
resulted in an increase in
their r-2 values of about 4% over the individual
estimations.
Although all 3 reference branches provided reasonably good estimations (t-2 ranging from .927 to ,985) the larger units resulted in
JOURNAL
OF RANGE
MANAGEMENT
38(5), September
1966
Table 1. Prediction equ8tions (Y = 8ctu8l weight in gnms, X = estimrted
weight in grams, V = unopy volume in cma), coefficients of determination
(rz), st8nd8rd error of. the estim8te (S y*x), coefficients of v8ri8tion
(C.V.), 8nd numberof mmples (N) for the reference unit 8nd dimension81
8rulysi.v methods of estim8ting junnu (ikfimosa twutist3puh~)bionuss.
Regression
Reference Unit
small unit2
Pooled data over
judges’
Averaged data over
judges4
large-compact
unit2
Pooled data over
judges
Averaged data over
judges
large-dispersed
unit2
Pooled data over
judges
Averaged data over
judges
Dimensional
Analysis
equation’
r*
Sy*x
C.V.
N
Y=-33.2+1.54(X)
.927
I42
27
45
Y=-59
.970
95
18
15
Y= 488+.851(x)
.954
II2
22
45
Y= 33.8+.878(X)
,985
68
I3
I5
Y= 23.7+.971(X)
.938
130
25
45
Y=
,979
80
I5
,948
126
24
+1.61(X)
2.3+1.01(X)
Y= 38.5+0.000359(V)
I5
I5
Literature Cited
‘None of the y intercepts are significantly different from zero (p>o.Ol).
*Significantly different at KO.05).
JCombin,ed individual data for the three judges.
‘Estimations
by the three judges
averaged
for each plant.
higher r* values, and the large-compacted
branch gave the highest
values. This supports the idea that there is an advantage to selecting a unit with an appearance closely resembling the foliage of the
shrubs being estimated.
Similar to jurema, the individual estimations
of the judges for
pau branco biomass could be combined into one regression equation (Table 2). The regression
analysis
showed the plant to unit
T8ble 2. Prediction equ8tions (Y = 8ctu8l weight in gr8ms, X = estim8ted
weight in gnms, V q c8nopy volume in cm’), coefficients of determin8tions (r2), st8nd8rd error of the estinmte (Sy-x), coefficients of v8ri8tion
(C.V.), 8nd number of cumples (N) for the reference plant 8nd dimension8l8tulysis
methods of estinuting p8u bmnco (Auxemma oncoca&)
Regression
equation’
Reference Unit
Pooled data over judges2
linear
Y=-829+.704(X)
quadratic
Y=-l31+1.2qx).00168(X2)
Averaged data over judges)
linear
Y= 35.7+.751(x)
quadratic
Y=-169+1.24(X).OOO174(X2)
Dimensional
analysis
Y= 95.7+.ooO886(V)
rr
Sy*x
C.V. N
.890
.933
213
I68
27
21
45
45
.949
.977
I51
107
I9
I3
I5
I5
,937
I61
20
I5
‘None
of the y intercepts are significantly different from zero (PX.05).
*Combined
individual
data of the three judges.
‘Estimations
by the three judges averaged for each plant.
ratio (P:U is the weight of the foliage of the test plant relative to the
weight of the foliage of the reference plant) had a significant
positive effect on the error of estimation (p q 0.008). Examination
of the residuals showed that more precise estimates were obtained
where the P:U was close to unity. There was a tendency to underestimate foliage biomass with higher P:U ratios. These results demonstrate the importance of selecting a reference plant similar in size
to the average plant being estimated.
The distance of the reference plant from the plants being estimated had no significant effect on the error of estimation @X.05).
For this study all plants were located within a convenient viewing
JOURNAL OF RANGE
MANAGEMENT
38(5),
September
distance from the reference plant (<I9 m). As with the reference
unit method, a slight increase in the coefficient of determination
was obtained
by fitting a regression equation
to the averaged
values of the 3 judges.
Measuring plant dimensions required about the same amount of
time in this study as sampling with a reference unit (about 1.5 min
per plant per person). The critical aspect of methodological
efficiency, however, is the development
of regressions to correct for
personal bias in the case of the reference unit technique and to
correlate dimensions with biomass in dimensional analysis. For the
latter method,
a specific regression
is required
for each species, and
possibly for different age classes and for different seasons within a
species to account for changes in foliage density. The bias of
estimation
in the reference unit method is a function of the personal characteristics
of the estimator, and a regression developed
to correct it could be applied to a group of species with similar
foliage appearance.
The generality of the bias for an individual
estimator
has not been tested by the authors but emerges as a
hypothesis on the basis of experience with several dozen students
learning the reference unit method.
Given that this approach
requires fewer regressions for field application
than dimensional
analysis, to achieve the same level of accuracy, the authors propose
that the most efficient procedure for biomass estimation would be
the reference unit method.
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